Systems of Equations Word Problems

Systems of Equations Word Problems

Solving Systems Word Problems

• Read the text (then re-read the text)

• Write a Let Statement

• Set up two (2) equations

• Solve the system using any method (graphing, elimination, or substitution)

• Answer the question

You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject?

You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject?

Multiple Choice

How many TOTAL problems do you have?

• 42

• 10

We don't know how many math or science problems so we are going to assign variables.

Science problems = x

Math problems = y

Fill in the Blank

How many total problems did we have?

Fill in the Blank

Using the information of 42 total problems, and our variables x & y write an equation that represents adding up all of our total problems. Do not include any spaces in your answer.

So our first equation is x+y=42.

Fill in the Blank

What's the 2nd equation? Remember, you have 10 more math problems than science problems.

Science problems = x

Math problems = y

Do not include any spaces in your answer.

Our second equation is y=x+10

Poll

Now it's time to solve the system. Which method would you use to solve

 $x+y=42$  
 $y=x+10$  

• Graphing

• Elimination

• Substitution

Fill in the Blank

How many science problems are there? Write only a number as your answer. Remember, 

x = science problems

y = math probems

 $x+y=42$  
 $y=x+10$  

Fill in the Blank

How many math problems are there? Write only a number as your answer. Remember, 

x = science problems

y = math problems

 $x+y=42$  
 $y=x+10$  

Multiple Choice

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

• t: # of tacos

  m: # of glasses of milk

• t: Cost of each taco

  m: Cost of each glass of milk

• t: total cost

  m: # of food items

• t: Cost of each glass of milk

  m: Cost of each taco

Multiple Choice

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38

  2s + 3c = 52

• 3s + 1c = 38

  3s + 2c = 52

• s + c = 38

  s + c = 52

• 3s + 3c = 38

  1s + 2c = 52

Multiple Choice

Beth and Nora each improved their yards by planting rose bushes and ornamental grass. They bought their supplies from the same store. Beth spent $36 on 6 rose bushes and 2 bunches of ornamental grass. Nora spent $66 on 4 rose bushes and 6 bunches of ornamental grass. Which equations could you use to solve this system?

• $36+6x=2y$
  $66+4x=6y$
  

• $6x+2y=36$
  $4x+6y=66$
  

• $6x-2y=36$
  $4x-6y=66$
  

• $y=8x+36$
  $y=10x+66$
  

Multiple Choice

Beth and Nora each improved their yards by planting rose bushes and ornamental grass. They bought their supplies from the same store. Beth spent $36 on 6 rose bushes and 2 bunches of ornamental grass. Nora spent $66 on 4 rose bushes and 6 bunches of ornamental grass. What is the cost of one rose bush and the cost of one bunch of ornamental grass?

• rose bush: $1, bunch of ornamental grass: $10

• rose bush: $4, bunch of ornamental grass: $7

• rose bush: $3, bunch of ornamental grass: $9

• rose bush: $2, bunch of ornamental grass: $5

Multiple Choice

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

• 3x + 2y = 315

  2x + 4y = 450

• 3x + 2y = 450

  2x + 4y = 315

• 2x + 2y = 315

  3x + 4y = 450

Multiple Choice

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. How long does it take her to do a haircut?

3x + 2y = 315

2x + 4y = 450

• 45 minutes

• 90 minutes

• 60 minutes

• 30 minutes

Multiple Choice

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?

• 20 Multiple Choice

• 10 Multiple Choice

• 15 Multiple Choice

• 5 multiple choice